Calculus of variations MOC

Functional derivative

Let 𝑉 be a function space over 𝕂 and 𝐹 :𝑉 →𝕂 be functional. The functional derivative or Euler operator¹ at 𝑓

𝛿𝐹𝛿𝑓∈𝑉

is a function such that

𝛿𝐹[𝑓;𝜂]=∫cod⁡𝑉𝛿𝐹𝛿𝑓𝜂𝑑𝑥

for all 𝜂 satisfying certain boundary conditions. We informally identify 𝜂 with 𝛿𝑓 to get a more intuitive expression.

---

develop | en | SemBr

Footnotes

1. 2004. Calculus of variations I, p. 18 ↩